1. Field of the Invention
The present invention relates to a method of simulating the shape of a sample after surface reaction processing, more particularly relates to a method of simulating the shape of a sample after chemical vapor deposition (CVD), etching, or other surface reaction processing. Further, the present invention relates to an apparatus for simulation capable of suitably executing this method of simulation and to a recording medium in which a program of the method of simulation is stored.
2. Description of the Related Art
In the steps for manufacture of a semiconductor device, CVD and dry etching are wildly used methods. In recent years, semiconductor devices have been required to exhibit increasingly high performance such as higher speeds, higher degrees of integration, and greater miniaturization. The control of the CVD and other steps has therefore become very important for increasing the reliability of the steps and enhancing the manufacturing yield etc. of the semiconductor devices to be manufactured.
CVD is a method where a silicon wafer or other sample is placed in a reaction chamber, a material gas is introduced, and the temperature is raised so as to initiate a chemical reaction of the material gas and thereby cause a desired thin layer such as a silicon oxide layer or a silicon nitride layer to deposit on the surface of the sample. For example, in order to cause a silicon oxide layer to deposit, a gas containing silane and oxygen etc. is introduced. As the CVD, various methods such as atmospheric pressure CVD, low pressure CVD, and plasma enhanced CVD have been known.
Dry etching is a method where a silicon wafer or other sample is placed in an evacuated reaction chamber, an etching gas is introduced, high frequency power is applied to cause a discharge and generate plasma, and ions and radicals produced in the plasma are made to strike the surface of the sample so as to cause a chemical reaction and etching. For example, the fluorine radicals produced from carbon tetrafluoride are radicals having a very high reactivity and can etch a silicon layer and silicon oxide layer. As the dry etching, a variety of methods such as plasma etching, chemical dry etching, or reactive ion etching have been known.
The partial pressure of the material gas in CVD or the etching gas in the dry etching process (hereinafter these gases will be referred to together as the "reaction gas") at the surface of the sample of the semiconductor wafer or the like (hereinafter simply referred to as the surface of the sample)is frequently lower than the gas pressure in the vicinity of the gas feed port of the chamber.
FIG. 1 shows the flow of the reaction gas in a chamber when processing such as CVD or etching is carried out. The reaction gas fed from a gas feed port 60 is deposited due to the chemical reaction or consumed due to the surface reaction such as etching on the surface of the sample 63, therefore the reaction gas flows in a direction 62 from the chamber to the surface of the sample 63. The unreacted reaction gas and gas generated due to the surface reaction are exhausted to the exhaust port for adjusting the pressure in the chamber, so the gas flows in the direction indicated by an arrow 61 in the entire chamber along with this. Due to the resistance of this flow, the partial pressure of the reaction gas at the surface of the sample is lowered.
FIG. 2 is a graph of the relationship between the partial pressure of the reaction gas and the distance from the surface of the sample. It indicates that the partial pressure of the reaction gas is a pressure P.sub.0 in the vicinity of the reaction gas feed port, but becomes gradually lower from the reaction gas feed port nearer to the surface of the sample and becomes the pressure P.sub.S at the surface of the sample.
The amount of reduction of the partial pressure of the reaction gas at the surface of the sample from the partial pressure at the reaction gas feed port depends upon the resistance of the chamber and the magnitude of the flow of the reaction gas. The resistance of the chamber does not change much at all in a process such as the CVD process, but the magnitude of the flow of the reaction gas changes considerably according to the amount of consumption of molecules of reaction gas at the surface of the sample. For this reason, the partial pressure of the reaction gas at the surface of the sample can change during a process such as the CVD process.
The reaction rate at the surface of the sample, that is, the deposition rate in the CVD process or the etching rate in the etching process, depends upon the number of molecules of the reaction gas striking the surface of the sample, that is, the partial pressure of the reaction gas at the surface of the sample. Accordingly, it is very important in a simulation of the shape of the sample after CVD, etching, or other processing to find the partial pressure of the reaction gas at the surface of the sample.
The following methods have been considered to deal with the effect of transport of the reaction gas in the chamber In the simulation of the shape of the sample after CVD, etching, or other processing.
1. Method Not Taking into Account the Effect of the Transport of the Reaction Gas in the Gas Phase
The simplest method is the method of ignoring the effect of the transport of the reaction gas in the gas phase. The partial pressure of the reaction gas in the chamber is sufficiently low, so there is no problem where the mean free path of the molecules of the reaction gas is larger than the chamber.
2. Method of Taking Into Account up to the Transport of the Reaction Gas in the Gas Phase
The reaction at the surface of the sample and the flow of the reaction gas in the chamber are simultaneously simulated, the partial pressure of the reaction gas at the surface of the sample is found, and the shape of the sample after processing is simulated.
3. Method of Calculating the Reduction of the Partial Pressure from the Flow of the Reaction Gas Assumed in Advance
This is a method of finding the partial pressure of the reaction gas at the surface of the sample by using the rate of growth found from experiments on the growth of layer on the surface of a flat sample.
In the three types of methods described above, however, there are the following problems. First, in the method not taking into account the effect of the transport of the reaction gas in the gas phase, when the mean free path of the molecules of the reaction gas is not larger than the chamber, an effect which cannot be ignored appears in the simulation of the shape of the sample after processing and correct simulation becomes difficult.
The method taking into account up to the transport of the reaction gas in the gas phase has the problem that a very long time is taken for the simulation. This is because, contrary to the simulation of the shape of the sample after processing paying attention to the micro region (for example, about a few microns), for the transport of the reaction gas in the gas phase in the chamber, it is necessary to take the macro region into account. For this reason, enormous calculations have to be carried out and there is much waste. For example, taking into account the transport of the reaction gas in the gas phase in a chamber requires solution of a fluid equation (Navier-Stokes' equation) or use of the Monte-Carlo method, but both suffer from the problem of long time calculation.
The method of calculating the reduction of the partial pressure from the flow of the reaction gas assumed in advance has the advantage that the time taken for calculation is not long like the above, but in actual layer forming processing, the layer is formed not on a flat surface, but on an even surface, and, the surface area of the layer-forming surface changes along with the elapse of time. Therefore, the surface area of the flat sample used in the experiment on the partial pressure of the reaction gas found by this method and the actual surface area of the layer-forming surface are different. As a result, there is a problem that the estimate of the partial pressure of the reaction gas at the surface of the sample is not correct.